Myelosuppression is one of the most common and severe adverse events associated with anti-cancer therapies and can be a source of drug attrition. Current mathematical modeling methods for assessing cytopenia risk rely on indirect measurements of drug effects and primarily focus on single lineage responses to drugs. However, anti-cancer therapies have diverse mechanisms with varying degrees of effect across hematopoietic lineages. To improve predictive understanding of drug-induced myelosuppression, we developed a quantitative systems pharmacology (QSP) model of hematopoiesis in vitro for quantifying the effects of anti-cancer agents on multiple hematopoietic cell lineages. We calibrated the system parameters of the model to cell kinetics data without treatment and then validated the model by showing that the inferred mechanisms of anti-proliferation and/or cell-killing are consistent with the published mechanisms for three classes of drugs with different mechanisms of action. Using a set of compounds as a reference set, we then analyzed novel compounds to predict their mechanisms and magnitude of myelosuppression. Further, these quantitative mechanisms are valuable for the development of translational in vivo models to predict clinical cytopenia effects.